Delete based on composite key from another table

Which DBMS is it? If it is in oralce then pairwise comparison should work.

DELETE FROM Table1
WHERE (Col1, Col2) IN
(SELECT Col1, Col2
 FROM Table2)

If it is SQL server then Michael's solution should work.

This can be cleanly performed using JOIN with your DELETE:

DELETE a
FROM 
    Table1 a 
    JOIN Table2 b
        ON a.Col1 = b.Col1
        AND a.Col2 = b.Col2